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Source: STEMS 2023 Maths CAT A Part B P5

January 8, 2023
geometrySTEMSradical axiscollinearity

Problem Statement

A convex quadrilateral ABCDABCD is such that ∠B=∠D\angle B = \angle D and are both acute angles. EE is on ABAB such that CB=CECB = CE and FF is on ADAD such that CF=CDCF = CD. If the circumcenter of CEFCEF is O1O_1 and the circumcenter of ABDABD is O2O_2. Prove that C,O1,O2C,O_1,O_2 are collinear.
Proposed by Kapil Pause
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